Solve for $x$ and $y$ using elimination. ${-x-6y = -39}$ ${x-5y = -16}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -55$ $\dfrac{-11y}{{-11}} = \dfrac{-55}{{-11}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-x-6y = -39}\thinspace$ to find $x$ ${-x - 6}{(5)}{= -39}$ $-x-30 = -39$ $-x-30{+30} = -39{+30}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {x-5y = -16}\thinspace$ and get the same answer for $x$ : ${x - 5}{(5)}{= -16}$ ${x = 9}$